Personally, I would recommend watching anything in the UC Timeline in chronological order, or at least in terms of release, through Char's Counterattack. I haven't seen anything after that, but from my understand those series (Gundam, Zeta, ZZ and Char's Counterattack) build off of each other in some way and it would be best to watch those in order.
Otherwise, I don't really think it matters. Sure, other series take aspects of the original show (the Char archetype, as mentioned above, being a big one) but it doesn't really matter, unless you really feel that you need/really want to know the basis of said archetypes before experiencing them.
If you like the super robot genre (and the Devil Gundam design), I'd almost suggest starting with that. I believe it's the only super robot show of Gundam metaseries and could be a good introduction for you. Of course, since you are already interested, starting with the original is good, too.
As for the side stuff in the sense of manga, etc. I haven't read any of them (well, I did read the original novels by Tomino, but those aren't canonical, so I'm not sure they count), but it hasn't stopped me from like/understanding/enjoying any of the series that I have watched. If you're really into a particular series and want more from it, then I'm sure it would be great to track them down... not sure about the ease, though.
There's a lot of Gundam I haven't seen and that's almost the glory of it. You still have a lot of entertaining shows without needing to track everything down, but it's all there if you want it.